Application d'une méthode d'éléments finis d'ordre un à la résolution numérique des équations de Navier-Stokes PDF Download
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Author: François Thomasset
Publisher:
ISBN:
Category :
Languages : fr
Pages : 70
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Book Description
Author: François Thomasset
Publisher:
ISBN:
Category :
Languages : fr
Pages : 70
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Book Description
Author: Vivette Girault
Publisher: Springer Science & Business Media
ISBN: 3642616232
Category : Mathematics
Languages : en
Pages : 386
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Book Description
The material covered by this book has been taught by one of the authors in a post-graduate course on Numerical Analysis at the University Pierre et Marie Curie of Paris. It is an extended version of a previous text (cf. Girault & Raviart [32J) published in 1979 by Springer-Verlag in its series: Lecture Notes in Mathematics. In the last decade, many engineers and mathematicians have concentrated their efforts on the finite element solution of the Navier-Stokes equations for incompressible flows. The purpose of this book is to provide a fairly comprehen sive treatment of the most recent developments in that field. To stay within reasonable bounds, we have restricted ourselves to the case of stationary prob lems although the time-dependent problems are of fundamental importance. This topic is currently evolving rapidly and we feel that it deserves to be covered by another specialized monograph. We have tried, to the best of our ability, to present a fairly exhaustive treatment of the finite element methods for inner flows. On the other hand however, we have entirely left out the subject of exterior problems which involve radically different techniques, both from a theoretical and from a practical point of view. Also, we have neither discussed the implemen tation of the finite element methods presented by this book, nor given any explicit numerical result. This field is extensively covered by Peyret & Taylor [64J and Thomasset [82].
Author: F. Thomasset
Publisher: Springer Science & Business Media
ISBN: 3642870473
Category : Science
Languages : en
Pages : 168
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Book Description
In structure mechanics analysis, finite element methods are now well estab lished and well documented techniques; their advantage lies in a higher flexibility, in particular for: (i) The representation of arbitrary complicated boundaries; (ii) Systematic rules for the developments of stable numerical schemes ap proximating mathematically wellposed problems, with various types of boundary conditions. On the other hand, compared to finite difference methods, this flexibility is paid by: an increased programming complexity; additional storage require ment. The application of finite element methods to fluid mechanics has been lagging behind and is relatively recent for several types of reasons: (i) Historical reasons: the early methods were invented by engineers for the analysis of torsion, flexion deformation of bearns, plates, shells, etc ... (see the historics in Strang and Fix (1972) or Zienckiewicz (1977». (ii) Technical reasons: fluid flow problems present specific difficulties: strong gradients,l of the velocity or temperature for instance, may occur which a finite mesh is unable to properly represent; a remedy lies in the various upwind finite element schemes which recently turned up, and which are reviewed in chapter 2 (yet their effect is just as controversial as in finite differences). Next, waves can propagate (e.g. in ocean dynamics with shallowwaters equations) which will be falsely distorted by a finite non regular mesh, as Kreiss (1979) pointed out. We are concerned in this course with the approximation of incompressible, viscous, Newtonian fluids, i.e. governed by N avier Stokes equations.
Author: Marc Bredif
Publisher:
ISBN:
Category :
Languages : fr
Pages : 133
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Book Description
RESOLUTION DES EQUATIONS DE NAVIER STOKES PAR UNE METHODE D'ELEMENTS FINIS MIXTES EN FONCTION COURANT PSI ET FONCTION TOURBILLON OMEGA . ON CONSIDERE PLUSIEURS TYPES DE CONDITIONS AUX LIMITES INHOMOGENES. LA PRESSION TOTALE EST INTRODUITE EN TANT QUE MULTIPLICATEUR DE LAGRANGE ASSOCIE A LA CONTRAINTE SUR LA VITESSE DIV U=0, CE QUI PERMET D'ASSOCIER A LA FORMULATION EN (PSI , OMEGA ) UNE FORMULATION DONNANT LA PRESSION TOTALE P*. PRESENTATION D'UNE METHODE DE CORRECTION POUR LE PROBLEME DES OSCILLATIONS NUMERIQUES DUES A LA NATURE DIFFUSIVE CONVECTIVE DES EQUATIONS DE NAVIER STOKES. L'ALGORITHME DE RESOLUTION ET FONDE SUR UNE METHODE DE GRADIENTS CONJUGUES. APPLICATION AUX ECOULEMENTS DANS UNE CAVITE CARNEE, AUTOUR D'UN CYLINDRE CIRCULAIRE ET D'UN PROFIL SYMETRIQUE A INCIDENCE NULLE
Author: Caterina Calgaro
Publisher:
ISBN:
Category :
Languages : fr
Pages : 179
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Book Description
CE TRAVAIL PORTE SUR LA DECOMPOSITION DE LA SOLUTION D'UN SYSTEME D'EQUATIONS AUX DERIVEES PARTIELLES EN SES GRANDES STRUCTURES ET DANS LEURS CORRECTIONS (METHODE DE TYPE INCREMENTAL), DANS LE CADRE D'UNE DISCRETISATION PAR ELEMENTS FINIS EN BASE HIERARCHIQUE. DANS LA PREMIERE PARTIE NOUS INTRODUISONS UNE APPROCHE NOUVELLE EN NEGLIGEANT LES VARIATIONS EN TEMPS DES TERMES D'INTERACTION ENTRE LES DIFFERENTES STRUCTURES. L'APPLICATION NUMERIQUE EST FAITE SUR LE PROBLEME DE BURGERS VISQUEUX BIDIMENSIONNEL. LES COMPOSANTES HIERARCHIQUES DU CHAMP DE VITESSE SONT TRAITEES DIFFEREMENT, AFIN DE METTRE EN PLACE UN ALGORITHME MULTI-NIVEAUX EN ESPACE ET EN TEMPS. NOUS DEDUISONS PLUSIEURS ESTIMATIONS A PRIORI SUR L'ERREUR INTRODUITE DANS LES EQUATIONS APPROCHEES. DANS LA DEUXIEME PARTIE NOUS GENERALISONS CETTE METHODE A LA RESOLUTION NUMERIQUE DES EQUATIONS DE NAVIER-STOKES, EN VITESSE-PRESSION, GRACE A UNE METHODE DE PENALISATION. DANS LE PREMIER CHAPITRE, APRES AVOIR TESTE PLUSIEURS ELEMENTS, NOUS NOUS ORIENTONS VERS UNE FORMULATION 4P1-P1 ET UNE RESOLUTION DIRECTE, A CHAQUE PAS DE TEMPS, DU SYSTEME LINEAIRE ISSU DE LA PENALISATION DE LA PRESSION. LE DERNIER CHAPITRE EST UNE EXTENSION DES IDEES ET DES TECHNIQUES DE LA PREMIERE PARTIE. ON NE SAIT HIERARCHISER AISEMENT LES EQUATIONS QUE SUR DEUX NIVEAUX. L'INTRODUCTION D'UNE PRESSION AUXILIAIRE PERMET SEULEMENT D'ETENDRE LE PROCESSUS A UN NOMBRE QUELCONQUE DE NIVEAUX. UNE NOUVELLE APPROCHE PORTE SUR UN COUPLAGE DE LA HIERARCHISATION AVEC LA METHODE DE DECOMPOSITION DE DOMAINE. CELLE-CI PERMET NOTAMMENT DE LOCALISER LE TRAITEMENT DES INTERACTIONS ENTRE LES GRANDES ECHELLES ET LEURS CORRECTIONS
Author: R. Glowinski
Publisher: Springer Science & Business Media
ISBN: 3540775064
Category : Mathematics
Languages : en
Pages : 507
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Book Description
When Herb Keller suggested, more than two years ago, that we update our lectures held at the Tata Institute of Fundamental Research in 1977, and then have it published in the collection Springer Series in Computational Physics, we thought, at first, that it would be an easy task. Actually, we realized very quickly that it would be more complicated than what it seemed at first glance, for several reasons: 1. The first version of Numerical Methods for Nonlinear Variational Problems was, in fact, part of a set of monographs on numerical mat- matics published, in a short span of time, by the Tata Institute of Fun- mental Research in its well-known series Lectures on Mathematics and Physics; as might be expected, the first version systematically used the material of the above monographs, this being particularly true for Lectures on the Finite Element Method by P. G. Ciarlet and Lectures on Optimization—Theory and Algorithms by J. Cea. This second version had to be more self-contained. This necessity led to some minor additions in Chapters I-IV of the original version, and to the introduction of a chapter (namely, Chapter Y of this book) on relaxation methods, since these methods play an important role in various parts of this book.
Author: Philippe G. Ciarlet
Publisher: SIAM
ISBN: 0898715148
Category : Mathematics
Languages : en
Pages : 552
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Book Description
This is the only book available that fully analyzes the mathematical foundations of the finite element method. Not only is it valuable reference and introduction to current research, it is also a working textbook for graduate courses in numerical analysis, including useful figures and exercises of varying difficulty.
Author: P.G. Ciarlet
Publisher: Elsevier
ISBN: 0080875254
Category : Mathematics
Languages : en
Pages : 551
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Book Description
The objective of this book is to analyze within reasonable limits (it is not a treatise) the basic mathematical aspects of the finite element method. The book should also serve as an introduction to current research on this subject. On the one hand, it is also intended to be a working textbook for advanced courses in Numerical Analysis, as typically taught in graduate courses in American and French universities. For example, it is the author's experience that a one-semester course (on a three-hour per week basis) can be taught from Chapters 1, 2 and 3 (with the exception of Section 3.3), while another one-semester course can be taught from Chapters 4 and 6. On the other hand, it is hoped that this book will prove to be useful for researchers interested in advanced aspects of the numerical analysis of the finite element method. In this respect, Section 3.3, Chapters 5, 7 and 8, and the sections on "Additional Bibliography and Comments should provide many suggestions for conducting seminars.
Author: BRIGITTE.. IBLER
Publisher:
ISBN:
Category :
Languages : fr
Pages : 81
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Book Description
FORMULATION VITESSE-PRESSION. PROPOSITION D'UNE METHODE DE RESOLUTION BASEE SUR LE TRAITEMENT SEPARE DES TERMES CONVECTIFS. CE PROCEDE PERMET DE PRENDRE EN COMPTE LE CARACTERE HYPERBOLIQUE DE LA CONVECTION ET PAR CONSEQUENT D'OBTENIR DES RESULTATS POUR DES NOMBRES DE REYNOLDS ELEVES. L'EQUATION DE CONVECTION EST RESOLUE PAR UNE METHODE DES CARACTERISTIQUES. ETUDE DU PROBLEME DE STOKES. LES SYSTEMES LINEAIRES SONT RESOLUS PAR UNE METHODE DE GRADIENT CONJUGUE PRECONDITIONNE. RESULTATS NUMERIQUES POUR UNE CAVITE AUX PAROIS MOBILES, UN JET ENTRANT DANS UNE CAVITE ET L'ECOULEMENT AUTOUR D'UN CYLINDRE
Author: Seymour V. Parter
Publisher: Elsevier
ISBN: 1483277836
Category : Technology & Engineering
Languages : en
Pages : 337
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Book Description
Large Scale Scientific Computation is a collection of papers that deals with specialized architectural considerations, efficient use of existing computers, software developments, large scale projects in diverse disciplines, and mathematical approaches to basic algorithmic problems. One paper describes numerical treatment of large highly nonlinear two or three dimensional boundary value problems by quadratic minimization techniques applied in many institutions such as in Laboratoire Central des Ponts et Chaussees, Avions Marcel Dassault et Breguet Aviation. Another paper discusses computer-structured design techniques to improve the reliability, efficiency, and accuracy of future production codes. Computer modelling is a potent tool in numerical weather prediction relying on observation, analysis, initialization, and model development. One paper illustrates a systolic algorithm for matrix triangulation, as well as its uses in the Cholesky decomposition of covariance matrices. Another paper describes the Transient Reactor Analysis Code (TRAC) designed to deal with internal flow problems of nuclear reactors. One paper explains the application of large-scale aerodynamic simulation where the programmer can use finite difference techniques in which a large number of mesh points are strategically and orderly placed in the domain of the flow field. The collection is intended for undergraduates in mathematics, programming, computer science, or engineering courses, and designers or researchers involved in industrial facilities, aeronautics, and nuclear design.
